论文标题
在保守噪声下孤立的谐波网络的热化
Thermalization of isolated harmonic networks under conservative noise
论文作者
论文摘要
我们研究具有成对相互作用和二进制碰撞规则的标量谐波网络，交换了随机选择的几个站点的动量。我们考虑了总能量保存的孤立网络的情况。在第一部分中，我们将动力学作为正常模式（或动作角度）坐标中的随机图重新铸造，并提供对其的几何解释。我们为通用网络提出问题，但为了完整性，还要重新考虑翻译不变的晶格。在第二部分中，我们检查了动力学极限及其有效性范围。从网络的本征态表示线性碰撞运算符的一般形式。这定义了一个\ textit {Action Network}，其连通性提供了有关不平衡动力学的信息。我们提供了一些示例（有序和无序的链条和弹性网络），其中可以以整洁的方式确定动作空间中连接的拓扑。作为一种应用，我们将放松的经典问题从线性动作的动力学的角度来对待。我们用数值模拟比较了基于碰撞算子的光谱的结果，该结果是基于新的方案基于正常模式坐标的运动方程的新方案进行的。
We study a scalar harmonic network with pair interactions and a binary collision rule, exchanging the momenta of a randomly-chosen couple of sites. We consider the case of the isolated network where the total energy is conserved. In the first part, we recast the dynamics as a stochastic map in normal modes (or action-angle) coordinates and provide a geometric interpretation of it. We formulate the problem for generic networks but, for completeness, also reconsider the translation-invariant lattices. In the second part, we examine the kinetic limit and its range of validity. A general form of the linear collision operator in terms of eigenstates of the network is given. This defines an \textit{action network}, whose connectivity gives information on the out-of-equilibrium dynamics. We present a few examples (ordered and disordered chains and elastic networks) where the topology of connections in action spaces can be determined in a neat way. As an application, we consider the classic problem of relaxation to equipartition from the point of view of the dynamics of linear actions. We compare the results based on the spectrum of the collision operator with numerical simulation, performed with a novel scheme based on direct solution of the equation of motion in normal modes coordinates.
